1 . A bitstring $b_1b_2{\dots}b_n$ of length $n$ is called a palindrome if $$ b_1b_2{\dots}b_{n-1}b_n = b_nb_{n-1}{\dots}b_2b_1, $$ i.e., reading the string from left to right gives the same result as reading the string from right to left.
Let $n \geq 2$ be an even integer. You are given a uniformly random bitstring of length $n$. What is the probability that this bitstring is a palindrome?